Saturday, June 28, 2008

GIGO


Eli has learned over the years that all sorts of strange people write the same paper, very long, very hard to follow and very wrong. These papers and their defenders play the Gallileo card early and often. No one can follow the algebra (these things always hide under a blizzard of algebraic incantation), but you can look at the assumptions, and when you do this carefully you find some amazing stuff, not believable, not correct, but amazin. The bunnies have been through this with Gerlich and Tscheuschner, had a neat recent dissection of the Robinson, Robinson and Soon OISM paper, and yr. humble hare dabbles in classical quantum numerology including this classic of the genre. A recent paper by Ferenc Miskolczi falls neatly into this category and has been adopted enthusiastically by the usual suspects. If you have trouble with the paper, Miklos Zagoni's web site might make it easier for you, but the rubber really meets the road in a number of web sites including a 309 and counting thread at the climate audit bulletin board and a four part analysis at Niche Modeling. There is also something worth looking at on 2nd Sex and Arthur Smith took a brief run at it in the comments at Rabett Run.

Before looking at the science, a reply by Nick Stokes (who carried much of the argument at CA) is worth quoting

Re: What do people think of this new paper?

by pliny on Tue Jun 03, 2008 5:56 am
alexharv074 wrote:Having searched the web far & wide I am unable to find that anyone has actually contradicted M on this point.
Have you found anyone who thinks it is right, and can explain why?

I think Miskolczi's paper could have been written in two sentences:
"The greenhouse gas theory that has been used for the last century is TOTALLY WRONG! The proof is left as an exercise for the reader."
Seriously, if you are making a claim like this, you need a good argument, put with some clarity. You would usually write down a model with some unknowns, state some physical principles with their resulting equations, and derive relations which characterise the unknowns. M does this, but at least three of his basic equations appear to be totally wrong. They actually look like elementary errors. Or if they are right, it seems no-one can explain them.

So this is Black Knight stuff. OK the use of Kirchhoff may be wrong, not sure about virial or that pesky Eq 7, but can anyone prove this is wrong, or that? People just lose patience.

Especially as these questions also come with no referencing or explanation. Who exactly is using Eddington's equation wrongly, and how? And re Qn 2, what on earth is that graph? It just says that he computed two sets of points which seem to align. He didn't say anything about how they were computed. What comment could be made?

Nick Stokes

Well you ask, where is the beef (which shows how old Eli is)?

A number of beefs there are with this paper which make it unnecessary to read through the whole thing, although some brave souls have done so multiple times. This includes Arthur Smith, Nick Stokes and David Stockwell, the proprietor of Niche Modeling. You can catch up with them at Niche Modeling or at the CA thread, links above.

It boils down to the following:

A. Miskolczi does not understand Kirchoff's Law. As Stokes puts it
His invocation of K’s Law isn’t saying that up and down radiation is equal. The balance at the surface is expressed in his Eq 2. What he is equating is down radiation E_D and an absorbance A. Why I say that this isn’t Kirchhoff is that, in any statement of K that I have seen, emissivity is equal to absorptivity. These are coefficients, properties of objects. A body has much the same emissivity regardless of how much it IR is emitting. But no, M equates an actual emittance E_D with an actual absorption A, which I think is quite wrong. He then says “The physical interpretations of these two equations may fundamentally change the general concept of greenhouse theories.”
There is a rather longer version of this at CA

Re: What do people think of this new paper?

by pliny on Sun May 11, 2008 5:21 am
I think Miskolczi's paper goes wrong in its treatment of Kirchhoff's Law. But firstly, I'd like to note some of the cogent objections made earlier in this thread. Hans Erren queries the grey-body assumption, which lead to some discussion. stevo and apsmith queried the virial theorem statement; apsmith followed it up with the author, without apparently a convincing reply. That looks odd to me too.

But my main sticking point was the use of Kirchhoff's law. Steve Milesworthy raised it here. He hoped it wouldn't affect the paper's conclusions, but I think it does. There was some discussion on equilibrium discussions later in the thread. I'll summarise the problem.

Miskolczi says, in Sec 3:
According to the Kirchhoff law, two systems in thermal equilibrium exchange energy by absorption and emission in equal amounts, therefore, the thermal energy of either system can not be changed.
That isn't the definition I know. Thermal equilibrium, at least as often interpreted, is very restrictive, and suggests no nett flux at all. The more usual criterion is Local Thermodynamic Equilibrium (LTE), which is generally thought to be true in the atmosphere, except at rarefied levels. And then, in Pierrehumbert's book
Kirchoff’s Law states that the emissivity of a substance at any given frequency equals the absorptivity measured at the same frequency....
We will content ourselves here with the statement that all known liquid and solid planetary materials, as well as the gases making up atmospheres, conform very well to Kirchoff’s Law, except perhaps in the most tenuous outer reaches of atmospheres where the gas itself is not in thermodynamic equilibrium.
Or in these online lecture notes
Kirchhoff’s law states that absorptivity and emissivity are always equal....
Kirchhoff’s law may be considered valid for all processes of relevance to the atmosphere.
Note that absorptivity and emissivity are properties of objects - they do not imply any particular absorption or emission. The absorption will depend on the incident radiation, and the emission will depend on the temperature.

But Miskolczi's Eq (4) is absolute. It says that the upward LW radiation absorbed is equal to the downward LW radiation, as a result of Kirchhoff's Law. This means that the downward radiation is independent of air temperature, and hence also, I think, of GHG content beyond a limit. This is why he gets the limit on the greenhouse effect. This statement is different from his conservation of energy statement there.

But you can see this is wrong by applying the same logic to other levels of the atmosphere - there is nothing special about the surface. At TOA, there is upward emitted LW radiation, clearly measurable; it is Eu in M's model. But there is no absorption of downward LW to balance it - because there is no downward LW at all (or only a tiny amount from the Sun).
B. Miskolczi claims a virial relationship between the IR emission from the surface, Su and the IR emission from the top of the atmosphere Eu. At best this is roughly true for the Earth's atmosphere as an experimental fact, but it is not a mathematical relationship. In essence, as Arthur Smith points out, this is a constraint that Miskolczi arbitrarily imposes on the Earth system

Re: What do people think of this new paper?

by apsmith on Wed Mar 12, 2008 7:22 am

Steveo, I think you've hit the nail on the head there.

I actually sent the author an email the other day asking that very question - how does he go from KE = PE/2 to Eu = Su/2? His response so far was not very clear, and included the word "guess" which left me a little concerned.

By adding in this relationship, Eu = Su/2, he overconstrains the problem, and that means you can get out of it just about any result you could wish, at least if you did a full analysis.

Eu is a flux of energy from the atmosphere into space - but he claims it "represents" the total kinetic energy of the atmosphere. Su is the flux of energy from the ground (at least, if going through his rather odd list of assumptions we take the point Su = Sg in his diagram figure 1), but he claims it "represents" the total gravitational potential energy, because the surface temperature is related to the total gravitational potential through the surface pressure and density.

He does not explicitly state any linear relationship or other analysis that justifies the Eu = Su/2 claim. Eu depends on the absorptive properties of the atmosphere and the vertical temperature profile, which doesn't seem to be derived or discussed here at all.

It does happen that for Earth, Eu is roughly half of the surface radiative flux, so Miskolczi's relationship roughly holds for our planet. But it sounds like he "guessed" that it was some sort of universal law based on looking at the parameters for Earth, rather than actually deriving it from the physics of the situation. At least I don't see any physical basis for the claim in this paper, and it's certainly not obvious from the meanings given to the terms here.
and

Re: What do people think of this new paper?

by apsmith on Wed Mar 12, 2008 11:51 am
You can compute total internal kinetic energy from the molecular formula for a gas - the average of 1/2 mv^2 = 3/2 kT. That means total kinetic energy = 3/2 n R T (n = number of moles of gas), or total kinetic energy = 3/2 P V (for a small region at constant pressure and temperature - you would need to integrate over the range of temperatures in the real atmosphere to get the proper number).

But what bearing does this have on outgoing thermal radiation (E_U) from the atmosphere? If the atmosphere absorbs most infrared radiation then there's going to be some rough top-level layer of the atmosphere (the photosphere) from which most of the outgoing thermal energy is coming; if temperature in this region is T_A then E_U would be given by the Stefan-Boltzmann relation, i.e. proportional to T_A^4. If the atmospheric temperature was roughly constant, that would give you an E_U value varying as (total kinetic energy)^4, rather than linearly, but then it also depends on the total mass of the atmosphere (the 'n' value above). In any case, the author's claim that E_U literally "represents" the total kinetic energy seems very far from reality.

I've exchanged some email with the author now, and it seems pretty clear he does not have an actual derivation of this relationship from physical principles. Rather he seems to have done some simulations relevant for Earth's atmosphere, noticed that this relationship roughly held, and then claimed this analogy to the virial relationship that has no actual basis in physics. As far as I can tell, anyway....
C. Pat Cassen has some additional problems with the mathematical analysis

16 comments:

Pat Cassen said...

Eli -

In addition to all of the above [misapplication of Kirkhoff’s Law, an unintelligible invocation of the virial theorem, and an incorrect and apparently inspirationally derived psuedo-energy equation (his eqn 7)], it appears that the linch-pin solution presented in Appendix B is not what it is claimed to be. It does not satisfy the required boundary conditions, nor does it have the properties required to produce Figure 3. These results appear to be the result of, let us say, an unconstrained approach to the math. But someone else might want to look into this, too.

Anonymous said...

The proof, as they say is in the pudding -- or in this case, in the earth's surface temperature.

All these "disproofs" of the greenhouse effect would be great if the earth did not actually show a greenhouse effect -- and if some very simple calculations did not actually give a fairly good approximation to the actual temperature impact of that effect (33K).

It doesn't even matter whether the virial theorem has been correctly applied or whether the algebra is correct.

In the absence of any connection with reality, this stuff is all basically just mathematical masturbation.

Arthur said...

Eli, thanks for gathering these arguments together. What the heck is "2nd sex" though and why does it have an analysis of this obscure climate paper? Weird stuff you find on the internets these days :-)

Magnus said...

Carrot on a string?
http://www.youtube.com/watch?v=YtdE662eY_M

EliRabett said...

Arthur, 2nd Sex is mostly about Second Life, but it is a cleaver play on Simone de Beauvoir's Second Sex, one of the foundations of modern feminism

Anonymous said...

I think it's worth mentioning that the Kirchoff's Law is derived from and dependent upon thermodynamic equilibrium. Emission and absorption are equal in thermodynamic equilibrium, but the surface of the Earth is not in thermal equilibrium and neither is most of the atmosphere.

It's easy to forget that point since the Earth's surface is in a more or less steady themal state - but one that is nonetheless far from equilibrium. The surface of the Earth is far from equilibrium because the radiation it absorbs has a far different spectrum than that it emits. It accepts low entropy radiation and emits much higher entropy radiation.

- CIP

EliRabett said...

Pig, you can measure a temperature at each of those points, which means that for all practical purposes you can use Kirchoff's law. You can't use it, for example in the ionosphere where you have trouble measuring a single temperature for all the components.

If I adopt your POV, I can't measure any meaningful temperature for the separate parts of the system. I can, you are wrong.

Anonymous said...

"The surface of the Earth is far from equilibrium because the radiation it absorbs has a far different spectrum than that it emits."

Presumably, that is a reference to this:

"A system is not in local thermodynamic equilibrium if the local kinetic (Maxwellian) temperature is not equal to the Planckian temperature of the radiation field."


In other words, even if the earth were a perfect black body, in order for it to be in strict "thermodynamic equilibrium" with its surrounding, the earth would have to be at about 5800K (the temp of the surface of the sun).

The problem, of course, is that this would violate energy conservation because the energy absorbed per unit time per unit area would then be very different (much less) than the energy emitted.

So the strict requirement for "thermodynamic equilibrium" is not of much (if any) use in this case. No surprise, really. Strict definitions almost never are. :)

Kirchoff's findings regarding black bodies (and gray bodies) are idealizations that apply to virtually nothing in the real world, strictly speaking.

But they come close enough in many instances to be useful. For example, it is useful to model the sun as a black body (at about 5800K) and it is also useful to model the earth as a gray body.

It may not be strictly true, but that does not mean one can not get a "good enough" answer in many cases by doing so.

To say that "Kirchoff's laws can not be used in this case because they only apply to strict thermodynamic equilibrium" is really not a very useful statement from a scientific standpoint.

A much more useful scientific statement would be that "Applying Kirchoff's laws in this case will lead to an error of x%"

If x happens to be "3", or 5 or even 10, one can be fairly confident that applying the law will give a "pretty good" answer.

On the other hand, if x is 30 or 50 or 150, we probably should not be using the laws at all for the case at hand.

I think a more fruitful avenue of dismissing Miskolczi's idea is just to see whether it jibes with experiment.

It certainly appears that it does not.


first there is the runaway greenhouse on Venus, which Miskolczi would seem to preclude (even though he says not -- with little more than a wave of the hand)

Second there is actually a regional tropical runaway greenhouse effect here on earth, which would also seem to be ruled out by Miskolczi.

In the latter case, there is obviously a limiting factor (keeping sea surface temp to 303K or less), but it is quite possible that it is loss of energy to the surroundings (carried away by ocean or atmospheric current, for example) rather than increased clouds (blocking incoming radiation) that is limiting.

The key thing is that in the latter case, Miskolczi would seem to preclude the amount of warming actually seen with this tropical runaway effect as well as the changes in the optical depth that are seen.

Anonymous said...

Actually, the fact that kirchoff's radiation laws can be applied even though strict thermodynamic equilibrium is not met is somewhat analogous to the application of the Kirchoff (scalar) diffraction theory to light.

The Kirchoff theory, which Kirchoff came up with for acoustic (scalar) waves works quite well for electromagnetic (vector) waves, as long as one does not need a solution within a few wavelengths of the diffracting object.

And Kirchoff's theory is one hell of a lot simpler than the vector theory, for which only a few exact solutions have been worked out.

It works, so people use it.

Philip Machanick said...

Here's another take on Kirchoff. It seems we should really be quoting Stewart's Law because Kirchoff got the detail wrong. Be that as it may, it's clear to me that the relevant physical law relates to the state of a single body as stated in the linked paper:

Formulated in 1858, Stewart’s Law [1] states that when an object is studied in thermal equilibrium, its absorption is equal to its emission.

If Miskolczi is making this claim without a citation, maybe he has found some other obscure “Kirchhoff law”. Or maybe he's just making this stuff up.

According to the Kirchhoff law, two systems in thermal equilibrium exchange energy by absorption and emission in equal amounts, therefore, the thermal energy of either system can not be changed.

Roger Abel, Norway said...

All claims on AGW happening on Earth rely upon correct collected measurement and calculations of the middle temperatures over the last 30 years by NOAA, GISS and CRU.

GET REAL FOLKS -these measurements are now proven to bee so heavily tampered with and systematically manipulated -they cannot be used as a "truth vitness" for the AGW claims anymore! (And you don't need a physics degree to find out)

The climate models also fall on this one, since they are derivated from the temperature trends and also uses them as initiation inputs -they're made to fit the FALSE temperature curve.


Who will be the first one to PROVE the claim that CO2 is a driving factor in the NOW hypotetically supposed AGW?

NONE OF YOU, I think!!!

Anonymous said...

Nick Stokes refuses to let Miskolczi respond. It's becoming very clear that RealClimate is totally agenda driven and not interested in science or honest discourse.

Criticisms of Miskolczi’s Law and the answers to them
http://miskolczi.webs.com/Answers_to_some_criticism.htm

Doc Savage Fan

EliRabett said...

Hi,

it turns out that all of the various reconstructions, GISSTemp, HadCRUT, NOAA, UAH, RSS, etc, all track each other amazingly well. The last two are satellite measurements from the lower troposphere, so that dog don't hunt.

More details and links here

EliRabett said...

Nick Stokes does not control the Real Climate Wiki.

Charles S. Opalek, PE said...

"At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity". First, our atmosphere is not a body or a surface. It is an ever-changing volume of transparent and non-transparent regimes with mass transport of solids, liquids and gases taking place within its own layers and with the solid changing albedo surface below. Second, how can thermal equilibrium be identified anywhere within this swirling, chaotic system? Everyone is throwing around Kirchoff's Law in their papers as if they have sole ownership of it.

Everyone is missing the big picture. Between 1880 and 2010, three global cooling and two global warming episodes have been identified which are in lock-step with total solar irradiance. Question: If CO2 is always increasing, then how can there be cooling? Answer: CO2 is irrelevant to cooling and warming. Stop analyzing the flea on the elephant's rear end and analyze the elephant in the room.

It is planetary mechanics which governs climate change; CO2 is just coming along for the ride. Brace yourselves for the Landscheidt Grand Solar Minimum we have entered and will be in for the next 60 years. In the near future all this CO2/AGW nonsense will become a distant memory.

Rocco said...

Charles S. Opalek: You are boring. How much will you bet?